Supernova (SN) explosions are the best candidates for being the engine of turbulence in galaxy discs, as they inject a huge amount of energy into the ISM.
The energy flux injected by SNe can be estimated from the observed SFR (\(\Sigma _\mathrm {SFR}\) ) using
\(\dot{E}_\mathrm {SNe} = \eta \Sigma _\mathrm {SFR} f_\mathrm {cc} E_\mathrm {SN}\) , where \(\eta \)  is SN efficiency (or coupling efficiency), \(E_\mathrm {SN}=10^{51}\)  erg is the energy of a single SN, and \(f_\mathrm {cc}\)  is the fraction of stars exploding as SN core-collapse given an initial mass function.
The key parameter is \(\eta \) , which is the fraction of the total SN energy that goes into feeding turbulence.
Analytical and numerical models of SN remnant evolution predict \(\eta \lesssim 0.1\) , as most of the SN energy is radiated away [1]}, [2]}.
To understand whether SNe can sustain the cold gas turbulence in galaxies, the expected SN energy must be compared to the observed kinetic energy density of the gas \(E_\mathrm {obs} = \frac{3}{2} \Sigma _\mathrm {obs} \sigma _\mathrm {obs}^2\) , with \(\Sigma _\mathrm {obs}\)  and \(\sigma _\mathrm {obs}\)  being the gas surface density and velocity dispersion.
[3]} used this approach to investigate the origin of the atomic gas turbulence in nearby galaxies, assuming \(L = 100\)  pc and \(\upsilon _\mathrm {turb}=10\)   km s\(^{-1}\) (i.e. \(\tau _\mathrm {diss}=10\)  Myr) across the disc.
They found that the SN energy can explain \(E_\mathrm {obs}\)  in the innermost regions of their galaxies, while very high (\(\eta \gg 0.1\) ) or even non-physical (\(\eta > 1\) ) efficiencies were needed in the outer parts where \(\Sigma _\mathrm {SFR}\)  is low [4]}.
Other mechanisms have been proposed, but no consensus has been reached about the main engine of turbulence [5]}.
